Extraction of tiled top-down irregular pyramids from large images

Transcription

1 Extraction of tiled top-down irregular pyramids from large images Romain Goffe 1 Guillaume Damiand 2 Luc Brun 3 1 SIC-XLIM, Université de Poitiers, CNRS, UMR6172, Bâtiment SP2MI, F-86962, Futuroscope Chasseneuil, France 2 LIRIS, Université Lyon, CNRS, UMR5205, Université Lyon 1, F-69622, Villeurbanne, France 3 GREYC, ENSICAEN, CNRS, UMR6072, 6 Boulevard du Maréchal Juin, F-14050, Caen, France February 21, 2011

2 1 Introduction and Context 2 Definition of a Tiled Topological Model 3 Application and Segmentation 4 Conclusion and Perspectives 2 / 19

3 1 Introduction and Context 2 Definition of a Tiled Topological Model 3 Application and Segmentation 4 Conclusion and Perspectives 3 / 19

4 Context Application ANR Project FoGrImMi: Search Through Large Microscopic Images Medical imaging (histology, cytology) Whole Slide Imaging for microscopical images Large multi-resolution images (30GB) Requirements: efficient tools for automatic analysis and processing of very large images. Objectives Define a top-down topological model Efficient update after splitting operations Hierarchical structure complying with causality principle Memory usage Constraints and proposed solutions Topological properties combinatorial maps Multi-resolution images hierarchical model Very large images top-down construction 4 / 19

5 Combinatorial and Topological Maps Combinatorial maps Dart: half-edge β 1 permutation: turns around a face β 2 involution: opposite face Topological maps Represent any partition Describe adjacency and inclusion relationships Efficient processing algorithms 5 / 19

6 Framework for Irregular Combinatorial Pyramids Definition Stack of combinatorial maps successively transformed. Bottom-up pyramids Main operation: merge Drawbacks: encode the whole initial partition high memory requirements Top-down pyramids Main operation: split Advantages: encode upper levels until given segmentation focus of attention 6 / 19

7 Top-down Pyramidal Model Definition Stack of topological maps Splitting operations from one level to another Up/down relations between darts and regions Causal structure Construction Copy: level duplication Link: hierarchical relations Refine: splitting operation use of segmentation criteria splitting: creates one region/pixel merging 7 / 19

8 Top-down Pyramidal Model Definition Stack of topological maps Splitting operations from one level to another Up/down relations between darts and regions Causal structure Construction Copy: level duplication Link: hierarchical relations Refine: splitting operation use of segmentation criteria splitting: creates one region/pixel merging 7 / 19

9 Top-down Pyramidal Model Definition Stack of topological maps Splitting operations from one level to another Up/down relations between darts and regions Causal structure Construction Copy: level duplication Link: hierarchical relations Refine: splitting operation use of segmentation criteria splitting: creates one region/pixel merging 7 / 19

10 Top-down Pyramidal Model Definition Stack of topological maps Splitting operations from one level to another Up/down relations between darts and regions Causal structure Construction Copy: level duplication Link: hierarchical relations Refine: splitting operation use of segmentation criteria splitting: creates one region/pixel merging 7 / 19

11 Top-down Pyramidal Model Definition Stack of topological maps Splitting operations from one level to another Up/down relations between darts and regions Causal structure Construction Copy: level duplication Link: hierarchical relations Refine: splitting operation use of segmentation criteria splitting: creates one region/pixel merging 7 / 19

12 Top-down Pyramidal Model Definition Stack of topological maps Splitting operations from one level to another Up/down relations between darts and regions Causal structure Construction Copy: level duplication Link: hierarchical relations Refine: splitting operation use of segmentation criteria splitting: creates one region/pixel merging 7 / 19

13 Top-down Pyramidal Model Definition Stack of topological maps Splitting operations from one level to another Up/down relations between darts and regions Causal structure Construction Copy: level duplication Link: hierarchical relations Refine: splitting operation use of segmentation criteria splitting: creates one region/pixel merging 7 / 19

14 1 Introduction and Context 2 Definition of a Tiled Topological Model 3 Application and Segmentation 4 Conclusion and Perspectives 8 / 19

15 Presentation Constraint Top-down construction only minimizes memory Application requires a bound memory usage Proposed solution Geometrical division of a map in topological tiles Insertions of fictive darts on the borders Integration in the pyramidal model New operator on darts for adjacent tiles connection Swap/load operations Incremental construction 9 / 19

16 Definitions Topological tile Topological tile t(i,j,k): partition of a geometrical subdivision (i,j) at level k t(i,j,k+1) deduced from t(i,j,k) by splitting operation Tiled top-down pyramid Tiled top-down pyramid: set of topological tiles Local pyramid: set of tiles loaded in memory 10 / 19

17 Connection of Adjacent Tiles Main steps Splitting borders ensures two adjacent tiles share the same number of darts on their borders Connection of the darts on shared border set β 2 relations Simplification step for minimality if the degree of a vertex equals 2 in both tiles 11 / 19

18 Extraction of a Tiled Pyramid Algorithm For each tile t(i, j, k) in level k: Load t(i 1, j, k + 1) and t(i, j 1, k + 1) Create t(i, j, k + 1) from t(i, j, k) Connect the neighbors of t(i, j, k + 1) Save t(i, j, k + 1), t(i 1, j, k + 1), t(i, j 1, k + 1) and t(i, j, k) Unload t(i 1, j, k + 1), t(i, j 1, k + 1) and t(i, j, k) Scanline extraction 4 tiles at most in memory 12 / 19

19 Extraction of a Tiled Pyramid Algorithm For each tile t(i, j, k) in level k: Load t(i 1, j, k + 1) and t(i, j 1, k + 1) Create t(i, j, k + 1) from t(i, j, k) Connect the neighbors of t(i, j, k + 1) Save t(i, j, k + 1), t(i 1, j, k + 1), t(i, j 1, k + 1) and t(i, j, k) Unload t(i 1, j, k + 1), t(i, j 1, k + 1) and t(i, j, k) Scanline extraction 4 tiles at most in memory 12 / 19

20 Extraction of a Tiled Pyramid Algorithm For each tile t(i, j, k) in level k: Load t(i 1, j, k + 1) and t(i, j 1, k + 1) Create t(i, j, k + 1) from t(i, j, k) Connect the neighbors of t(i, j, k + 1) Save t(i, j, k + 1), t(i 1, j, k + 1), t(i, j 1, k + 1) and t(i, j, k) Unload t(i 1, j, k + 1), t(i, j 1, k + 1) and t(i, j, k) Scanline extraction 4 tiles at most in memory 12 / 19

21 Extraction of a Tiled Pyramid Algorithm For each tile t(i, j, k) in level k: Load t(i 1, j, k + 1) and t(i, j 1, k + 1) Create t(i, j, k + 1) from t(i, j, k) Connect the neighbors of t(i, j, k + 1) Save t(i, j, k + 1), t(i 1, j, k + 1), t(i, j 1, k + 1) and t(i, j, k) Unload t(i 1, j, k + 1), t(i, j 1, k + 1) and t(i, j, k) Scanline extraction 4 tiles at most in memory 12 / 19

22 Extraction of a Tiled Pyramid Algorithm For each tile t(i, j, k) in level k: Load t(i 1, j, k + 1) and t(i, j 1, k + 1) Create t(i, j, k + 1) from t(i, j, k) Connect the neighbors of t(i, j, k + 1) Save t(i, j, k + 1), t(i 1, j, k + 1), t(i, j 1, k + 1) and t(i, j, k) Unload t(i 1, j, k + 1), t(i, j 1, k + 1) and t(i, j, k) Scanline extraction 4 tiles at most in memory 12 / 19

23 1 Introduction and Context 2 Definition of a Tiled Topological Model 3 Application and Segmentation 4 Conclusion and Perspectives 13 / 19

24 Criteria A B Figure: Basic segmentations for 4 levels pyramids. (A) Hierarchical criterion: standard deviation of up regions; (B) Colorimetric criterion: average gray levels comparison. Criteria can take into account: colorimetric features of regions topological features of a level hierarchical features of the pyramid 14 / 19

25 Construction from a Multi-resolution Image A B Figure: (A) Image resolutions; (B) Pyramid levels. Tiled structure fictive borders are displayed Multi-resolution images pyramid levels and image resolutions are independent notions Irregular pyramid irregular model within the tiles 15 / 19

26 Results Table: Memory usage: extraction for different scalings of image Lena. image tiles per memory disc side (px) level (MB) (MB) Extreme configuration: 4 levels 32K*32K Natural segmentation: lots of darts and regions Controlled memory usage 16 / 19

27 1 Introduction and Context 2 Definition of a Tiled Topological Model 3 Application and Segmentation 4 Conclusion and Perspectives 17 / 19

28 Conclusion Definition of a data structure topological representation hierarchical causal structure top-down construction Implementation based on topological maps tiled subdivision colorimetric, topological and hierarchical segmentation criteria integrated with multi-resolution images 18 / 19

29 Perspectives Segmentation aspect integration of clustering and quantization methods specific application to medical images Model improvements compare different strategies for the subdivision in tiles faster processing for very large images different splitting techniques multi-threading support 19 / 19